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<h1 class="title toc-ignore">Using the gpc package</h1>
<div id="introduction" class="section level2">
<h2>Introduction</h2>
<p>This package is presented as an accompaniment for the group project report for the COMPASS CDT, entitled <em>Pseudo-Marginal Inference for Gaussian Process Classification with Large Datasets</em>.</p>
<p>This package provides functionality to</p>
<ul>
<li>Choose an optimal subset of data that maximises the potential entropy score for a dataset, using the Information Vector Machine (IVM) algorithm (<code>ivm_subset_selection</code>)</li>
<li>Fit a Gaussian process classification model (<code>gpc</code>)</li>
<li>Plot, print and predict from this Gaussian process classification model ( <code>plot.gpc</code>, <code>print.gpc</code> and <code>predict.gpc</code>)</li>
</ul>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb1-1" data-line-number="1"><span class="kw">library</span>(gpc)</a>
<a class="sourceLine" id="cb1-2" data-line-number="2"><span class="co">#> Loading required package: mvtnorm</span></a></code></pre></div>
</div>
<div id="usage-on-the-spam-dataset" class="section level2">
<h2>Usage on the Spam Dataset</h2>
<p>In the report, we show that this classification model provides a more accurate classification of the binary problem encountered in the e-mail spam dataset. The problem is as follows: Given a large dataset of emails, with their corresponding word and character frequencies for different cases, can we accurately predict whether a particular e-mail is spam or not spam?</p>
<div id="loading-the-data-and-taking-a-subset" class="section level3">
<h3>Loading the Data and Taking a Subset</h3>
<p>We have provided access to the spam dataset as part of the package, which can be run with</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb2-1" data-line-number="1"><span class="kw">data</span>(spam)</a></code></pre></div>
<p>And format out the response and the predictor variables, as well as divide into testing and training datasets.</p>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb3-1" data-line-number="1">cut =<span class="st"> </span><span class="kw">round</span>(<span class="fl">0.6</span><span class="op">*</span><span class="kw">nrow</span>(spam))</a>
<a class="sourceLine" id="cb3-2" data-line-number="2">train_ind =<span class="st"> </span><span class="kw">sample</span>(<span class="dv">1</span><span class="op">:</span><span class="kw">nrow</span>(spam), cut)</a>
<a class="sourceLine" id="cb3-3" data-line-number="3">test_ind =<span class="st"> </span>(<span class="dv">1</span><span class="op">:</span><span class="kw">nrow</span>(spam))[<span class="op">-</span>train_ind]</a>
<a class="sourceLine" id="cb3-4" data-line-number="4">y =<span class="st"> </span>spam[train_ind, <span class="dv">1</span>]</a>
<a class="sourceLine" id="cb3-5" data-line-number="5">X =<span class="st"> </span>spam[train_ind, <span class="dv">2</span><span class="op">:</span><span class="kw">ncol</span>(spam)]</a>
<a class="sourceLine" id="cb3-6" data-line-number="6">yp =<span class="st"> </span>spam[test_ind, <span class="dv">1</span>]</a>
<a class="sourceLine" id="cb3-7" data-line-number="7">Xp =<span class="st"> </span>spam[test_ind, <span class="dv">2</span><span class="op">:</span><span class="kw">ncol</span>(spam)]</a></code></pre></div>
<p>The problematic part of fitting to this data immediately is its size:</p>
<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb4-1" data-line-number="1"><span class="kw">nrow</span>(X)</a>
<a class="sourceLine" id="cb4-2" data-line-number="2"><span class="co">#> [1] 2761</span></a></code></pre></div>
<p>Since we are using MCMC methods with a pseudo marginal approach, fitting to this data for a sufficient amount of iterations will be incredibly time consuming. We instead choose a subset which maximises the entropy score for a given subset size. We use the <code>ivm_subset_selection</code> function implemented here, and choose a subset size <span class="math inline">\(d=150\)</span>. We also need to specify the covariance function (or kernel) <span class="math inline">\(k\)</span>, as well as the initial values of the hyperparameter vector <span class="math inline">\(\boldsymbol{\theta}\)</span>, since these are used in the subset selection.</p>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb5-1" data-line-number="1">kernel =<span class="st"> </span><span class="cf">function</span>(x, y, theta) theta[<span class="dv">1</span>] <span class="op">*</span><span class="st"> </span><span class="kw">exp</span>(<span class="op">-</span><span class="fl">0.5</span> <span class="op">/</span><span class="st"> </span>theta[<span class="dv">2</span>]<span class="op">^</span><span class="dv">2</span> <span class="op">*</span><span class="st"> </span><span class="kw">sum</span>((x <span class="op">-</span><span class="st"> </span>y)<span class="op">^</span><span class="dv">2</span>))</a>
<a class="sourceLine" id="cb5-2" data-line-number="2">init_theta =<span class="st"> </span><span class="kw">c</span>(<span class="dv">1</span>, <span class="dv">1</span>)</a>
<a class="sourceLine" id="cb5-3" data-line-number="3">subset =<span class="st"> </span><span class="kw">ivm_subset_selection</span>(X, kernel, init_theta, <span class="dt">nsub =</span> <span class="dv">150</span>)</a></code></pre></div>
<p>Now we can specify the model matrix <span class="math inline">\(X\)</span> and response vector <span class="math inline">\(y\)</span> that we will use for training the classification model.</p>
<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb6-1" data-line-number="1">Xd =<span class="st"> </span>X[subset,]</a>
<a class="sourceLine" id="cb6-2" data-line-number="2">yd =<span class="st"> </span>y[subset]</a></code></pre></div>
</div>
<div id="fitting-the-model" class="section level3">
<h3>Fitting the Model</h3>
<p>The function <code>gpc</code> is a wrapper that calls the <code>Rcpp</code> functions that fit the classification model, including the pseudo marginal approximate likelihood and the Laplace approximation. These Rcpp functions are also written in parallel using <code>RcppParallel</code>, improving the speed of building the gram matrix <span class="math inline">\(K\)</span>, and calculating the pseudo marginal approximation.</p>
<p>We fit the model as follows:</p>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb7-1" data-line-number="1">gp_fit =<span class="st"> </span><span class="kw">gpc</span>(<span class="dt">y =</span> yd, </a>
<a class="sourceLine" id="cb7-2" data-line-number="2"> <span class="dt">X =</span> Xd, </a>
<a class="sourceLine" id="cb7-3" data-line-number="3"> <span class="dt">nsteps =</span> <span class="dv">500</span>,</a>
<a class="sourceLine" id="cb7-4" data-line-number="4"> <span class="dt">nburn =</span> <span class="dv">250</span>,</a>
<a class="sourceLine" id="cb7-5" data-line-number="5"> <span class="dt">nchains =</span> <span class="dv">2</span>,</a>
<a class="sourceLine" id="cb7-6" data-line-number="6"> <span class="dt">nimp =</span> <span class="dv">100</span>, </a>
<a class="sourceLine" id="cb7-7" data-line-number="7"> <span class="dt">init_theta =</span> <span class="kw">c</span>(<span class="dv">1</span>, <span class="dv">1</span>),</a>
<a class="sourceLine" id="cb7-8" data-line-number="8"> <span class="dt">kernel =</span> <span class="st">"gaussian"</span>,</a>
<a class="sourceLine" id="cb7-9" data-line-number="9"> <span class="dt">print_every =</span> <span class="ot">Inf</span></a>
<a class="sourceLine" id="cb7-10" data-line-number="10">)</a>
<a class="sourceLine" id="cb7-11" data-line-number="11"><span class="co">#> Fitting a GP classification model. </span></a>
<a class="sourceLine" id="cb7-12" data-line-number="12"><span class="co">#> Running with 2 chain, 500 steps. </span></a>
<a class="sourceLine" id="cb7-13" data-line-number="13"><span class="co">#> Data length n = 150, dimension p = 57.</span></a>
<a class="sourceLine" id="cb7-14" data-line-number="14"><span class="co">#> Number of hyperparameters: 2 </span></a>
<a class="sourceLine" id="cb7-15" data-line-number="15"><span class="co">#> _____________________________________ </span></a>
<a class="sourceLine" id="cb7-16" data-line-number="16"><span class="co">#> Chain 1 / 2 starting...</span></a>
<a class="sourceLine" id="cb7-17" data-line-number="17"><span class="co">#> Warning in algo_1(y, X, nsteps, nburn, nimp, init_theta, init_marginal_lik, :</span></a>
<a class="sourceLine" id="cb7-18" data-line-number="18"><span class="co">#> NAs introduced by coercion to integer range</span></a>
<a class="sourceLine" id="cb7-19" data-line-number="19"><span class="co">#> Chain 1 Running: 1/500 iterations completed. || Acceptance ratio: 0</span></a>
<a class="sourceLine" id="cb7-20" data-line-number="20"><span class="co">#> </span></a>
<a class="sourceLine" id="cb7-21" data-line-number="21"><span class="co">#> Chain completed successfully. </span></a>
<a class="sourceLine" id="cb7-22" data-line-number="22"><span class="co">#> Chain 2 / 2 starting...</span></a>
<a class="sourceLine" id="cb7-23" data-line-number="23"><span class="co">#> Warning in algo_1(y, X, nsteps, nburn, nimp, init_theta, init_marginal_lik, :</span></a>
<a class="sourceLine" id="cb7-24" data-line-number="24"><span class="co">#> NAs introduced by coercion to integer range</span></a>
<a class="sourceLine" id="cb7-25" data-line-number="25"><span class="co">#> Chain 2 Running: 1/500 iterations completed. || Acceptance ratio: 0</span></a>
<a class="sourceLine" id="cb7-26" data-line-number="26"><span class="co">#> </span></a>
<a class="sourceLine" id="cb7-27" data-line-number="27"><span class="co">#> Chain completed successfully.</span></a></code></pre></div>
<p>Most arguments are self explanatory, but for a description of all inputs to <code>gpc</code>, see <code>?gpc</code>. Note that we have only used 500 steps, and an <span class="math inline">\(Nimp\)</span> value of 200, which is lower than what is written into the report. When fitting the full model, higher values are used.</p>
<p>Now we can inspect the model using <code>plot.gpc</code>, an S3 method used for plotting <code>gpc</code> objects.</p>
<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb8-1" data-line-number="1"><span class="kw">plot</span>(gp_fit)</a></code></pre></div>
<p><img 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" /><!-- --> By default, <code>plot.gpc</code> will plot the trace and density plots of the hyperparameters and the log pseudo marginal likelihood approximation. The argument <code>f=TRUE</code> will plot a series of the same plots for the latent variables <span class="math inline">\(f\)</span>.</p>
</div>
<div id="predicting-from-the-model" class="section level3">
<h3>Predicting from the Model</h3>
<p>To obtain predictions from this fit, we can use <code>predict.gpc</code>, which averages across all values of hyperparameter vector <code>theta</code> across all samples and chains, to produce probabilities at each data point for the positive class.</p>
<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb9-1" data-line-number="1">pred_train =<span class="st"> </span><span class="kw">predict</span>(gp_fit, X)</a>
<a class="sourceLine" id="cb9-2" data-line-number="2"><span class="co">#> Warning in predict_gp(object$y, object$X, newdata, object$kernel,</span></a>
<a class="sourceLine" id="cb9-3" data-line-number="3"><span class="co">#> fit_all_chains, : NAs introduced by coercion to integer range</span></a>
<a class="sourceLine" id="cb9-4" data-line-number="4"><span class="co">#> Predicting from GP classification model. </span></a>
<a class="sourceLine" id="cb9-5" data-line-number="5"><span class="co">#> Averaging across all 500 steps, 2 chain(s). </span></a>
<a class="sourceLine" id="cb9-6" data-line-number="6"><span class="co">#> Fit Data length n = 150, dimension p = 57.</span></a>
<a class="sourceLine" id="cb9-7" data-line-number="7"><span class="co">#> New data length n = 2761, dimension p = 57.</span></a>
<a class="sourceLine" id="cb9-8" data-line-number="8"><span class="co">#> _____________________________________ </span></a>
<a class="sourceLine" id="cb9-9" data-line-number="9"><span class="co">#> </span></a>
<a class="sourceLine" id="cb9-10" data-line-number="10"><span class="co">#> Completed.</span></a></code></pre></div>
<p>Note that we fit the model to <code>Xd</code>, the subset model matrix, but predictions can be evaluated on the full training dataset. We do the same for the testing set.</p>
<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb10-1" data-line-number="1">pred_test =<span class="st"> </span><span class="kw">predict</span>(gp_fit, Xp)</a>
<a class="sourceLine" id="cb10-2" data-line-number="2"><span class="co">#> Warning in predict_gp(object$y, object$X, newdata, object$kernel,</span></a>
<a class="sourceLine" id="cb10-3" data-line-number="3"><span class="co">#> fit_all_chains, : NAs introduced by coercion to integer range</span></a>
<a class="sourceLine" id="cb10-4" data-line-number="4"><span class="co">#> Predicting from GP classification model. </span></a>
<a class="sourceLine" id="cb10-5" data-line-number="5"><span class="co">#> Averaging across all 500 steps, 2 chain(s). </span></a>
<a class="sourceLine" id="cb10-6" data-line-number="6"><span class="co">#> Fit Data length n = 150, dimension p = 57.</span></a>
<a class="sourceLine" id="cb10-7" data-line-number="7"><span class="co">#> New data length n = 1840, dimension p = 57.</span></a>
<a class="sourceLine" id="cb10-8" data-line-number="8"><span class="co">#> _____________________________________ </span></a>
<a class="sourceLine" id="cb10-9" data-line-number="9"><span class="co">#> </span></a>
<a class="sourceLine" id="cb10-10" data-line-number="10"><span class="co">#> Completed.</span></a></code></pre></div>
<p>From here, we can see the percentage of correct predictions in both cases (using a 0-1 loss, if the probabilities are greater than 0.5 then we predict the positive class, otherwise it is the negative class).</p>
<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb11-1" data-line-number="1">output_pred_train =<span class="st"> </span><span class="kw">ifelse</span>(pred_train <span class="op">></span><span class="st"> </span><span class="fl">0.5</span>, <span class="dv">1</span>, <span class="dv">-1</span>)</a>
<a class="sourceLine" id="cb11-2" data-line-number="2">output_pred_test =<span class="st"> </span><span class="kw">ifelse</span>(pred_test <span class="op">></span><span class="st"> </span><span class="fl">0.5</span>, <span class="dv">1</span>, <span class="dv">-1</span>)</a></code></pre></div>
<p>The percentages are given by</p>
<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb12-1" data-line-number="1"><span class="kw">table</span>(output_pred_train <span class="op">-</span><span class="st"> </span>y <span class="op">==</span><span class="st"> </span><span class="dv">0</span>)[<span class="dv">2</span>] <span class="op">/</span><span class="st"> </span><span class="kw">length</span>(y)</a>
<a class="sourceLine" id="cb12-2" data-line-number="2"><span class="co">#> TRUE </span></a>
<a class="sourceLine" id="cb12-3" data-line-number="3"><span class="co">#> 0.7921043</span></a>
<a class="sourceLine" id="cb12-4" data-line-number="4"><span class="kw">table</span>(output_pred_test <span class="op">-</span><span class="st"> </span>yp <span class="op">==</span><span class="st"> </span><span class="dv">0</span>)[<span class="dv">2</span>] <span class="op">/</span><span class="st"> </span><span class="kw">length</span>(yp)</a>
<a class="sourceLine" id="cb12-5" data-line-number="5"><span class="co">#> TRUE </span></a>
<a class="sourceLine" id="cb12-6" data-line-number="6"><span class="co">#> 0.8108696</span></a></code></pre></div>
</div>
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